Meanwhile, powerful variational tools have been developed in the last decade for studying mean-field interacting jump processes and their limits under the assumption of detailed balance. To highlight only a few: [1]} studied mean-field limits for measure-dependent jump processes; [2]} proved the convergence of the spatially-homogeneous Kac-process to the Boltzmann equation; [3]} investigated the macroscopic limit of Becker-Döring models; [4]} showed hydrodynamic limits for zero-range and exclusion processes; [5]} discussed convergence and higher-order approximations for chemical reaction networks, an approach that was subsequently used in the setting of discretized reaction-diffusion equations in [6]}.
